The Shift of the Baryon Acoustic Oscillation Scale: A Simple Physical Picture

A shift of the baryon acoustic oscillation (BAO) scale to smaller values than predicted by linear theory was observed in simulations. In this paper, we try to provide an intuitive physical understanding of why this shift occurs, explaining in more pedagogical detail earlier perturbation theory calculations. We find that the shift is mainly due to the following physical effect. A measurement of the BAO scale is more sensitive to regions with long wavelength overdensities than underdensities, because (due to non-linear growth and bias) these overdense regions contain larger fluctuations and more tracers and hence contribute more to the total correlation function. In overdense regions the BAO scale shrinks because such regions locally behave as positively curved closed universes, and hence a smaller scale than predicted by linear theory is measured in the total correlation function. Other effects which also contribute to the shift are briefly discussed. We provide approximate analytic expressions for the non-linear shift including a brief discussion of biased tracers and explain why reconstruction should entirely reverse the shift. Our expressions and findings are in agreement with simulation results, and confirm that non-linear shifts should not be problematic for next-generation BAO measurements.Comment: 10 pages, replaced with version accepted by Phys. Rev.

The Impact of Wrong Assumptions in BAO Reconstruction

The process of density field reconstruction enhances the statistical power of distance scale measurements using baryon acoustic oscillations (BAO). During this process a fiducial cosmology is assumed in order to convert sky coordinates and redshifts into distances; fiducial bias and redshift-space-distortion parameters are also assumed in this procedure. We analytically assess the impact of incorrect cosmology and bias assumptions on the post-reconstruction power spectra using low-order Lagrangian perturbation theory, deriving general expressions for the incorrectly reconstructed spectra. We find that the BAO peak location appears to shift only by a negligible amount due to wrong assumptions made during reconstruction. However, the shape of the BAO peak and the quadrupole amplitude can be affected by such errors (at the percent- and five-percent-level respectively), which potentially could cause small biases in parameter inference for future surveys; we outline solutions to such complications.Comment: 18 pages, 3 figures; comments welcome. v2 matches JCAP accepted versio

Reconstructing Small Scale Lenses from the Cosmic Microwave Background Temperature Fluctuations

Cosmic Microwave Background (CMB) lensing is a powerful probe of the matter distribution in the Universe. The standard quadratic estimator, which is typically used to measure the lensing signal, is known to be suboptimal for low-noise polarization data from next-generation experiments. In this paper we explain why the quadratic estimator will also be suboptimal for measuring lensing on very small scales, even for measurements in temperature where this estimator typically performs well. Though maximum likelihood methods could be implemented to improve performance, we explore a much simpler solution, revisiting a previously proposed method to measure lensing which involves a direct inversion of the background gradient. An important application of this simple formalism is the measurement of cluster masses with CMB lensing. We find that directly applying a gradient inversion matched filter to simulated lensed images of the CMB can tighten constraints on cluster masses compared to the quadratic estimator. While the difference is not relevant for existing surveys, for future surveys it can translate to significant improvements in mass calibration for distant clusters, where galaxy lensing calibration is ineffective due to the lack of enough resolved background galaxies. Improvements can be as large as $\sim 50\%$ for a cluster at $z = 2$ and a next-generation CMB experiment with 1$\mu$K-arcmin noise, and over an order of magnitude for lower noise levels. For future surveys, this simple matched-filter or gradient inversion method approaches the performance of maximum likelihood methods, at a fraction of the computational cost.Comment: 11 pages, 7 figure

A bias to CMB lensing measurements from the bispectrum of large-scale structure

The rapidly improving precision of measurements of gravitational lensing of the Cosmic Microwave Background (CMB) also requires a corresponding increase in the precision of theoretical modeling. A commonly made approximation is to model the CMB deflection angle or lensing potential as a Gaussian random field. In this paper, however, we analytically quantify the influence of the non-Gaussianity of large-scale structure lenses, arising from nonlinear structure formation, on CMB lensing measurements. In particular, evaluating the impact of the non-zero bispectrum of large-scale structure on the relevant CMB four-point correlation functions, we find that there is a bias to estimates of the CMB lensing power spectrum. For temperature-based lensing reconstruction with CMB Stage-III and Stage-IV experiments, we find that this lensing power spectrum bias is negative and is of order one percent of the signal. This corresponds to a shift of multiple standard deviations for these upcoming experiments. We caution, however, that our numerical calculation only evaluates two of the largest bias terms and thus only provides an approximate estimate of the full bias. We conclude that further investigation into lensing biases from nonlinear structure formation is required and that these biases should be accounted for in future lensing analyses.Comment: 15+19 pages, 9 figures. Comments welcom

Improving small-scale CMB lensing reconstruction

Over the past decade, the gravitational lensing of the Cosmic Microwave Background (CMB) has become a powerful tool for probing the matter distribution in the Universe. The standard technique used to reconstruct the CMB lensing signal employs the quadratic estimator (QE) method, which has recently been shown to be suboptimal for lensing measurements on very small scales in temperature and polarization data. We implement a simple, more optimal method for the small-scale regime, which involves taking the direct inverse of the background gradient. We derive new techniques to make continuous maps of lensing using this "Gradient-Inversion" (GI) method and validate our method with simulated data, finding good agreement with predictions. For idealized simulations of lensing cross- and autospectra that neglect foregrounds, we demonstrate that our method performs significantly better than previous quadratic estimator methods in temperature; at $L=5000-9000$, it reduces errors on the lensing auto-power spectrum by a factor of $\sim 4$ for both idealized CMB-S4 and Simons Observatory-like experiments and by a factor of $\sim 2.6$ for cross-correlations of CMB-S4-like lensing reconstruction and the true lensing field. We caution that the level of the neglected small-scale foreground power, while low in polarization, is very high in temperature; though we briefly outline foreground mitigation methods, further work on this topic is required. Nevertheless, our results show the future potential for improved small-scale CMB lensing measurements, which could provide stronger constraints on cosmological parameters and astrophysics at high redshifts